where \(\langle .\;, . \rangle \)  represents the dot product between learned embeddings. Here, we are performing softmax over sampled classes \(C_\mathcal {B}\)  instead of performing softmax over all the classes. The softmax over-sampled classes introduce sampling bias in the full softmax computation. This bias is corrected through the proposal distribution \(Q_p(e_i|q_i)\)  which is the probability of \(e_i\)  being included as a positive sample in the training batch. We utilize count-min sketch [1]} to estimate \(Q_p(e_i|q_i)\)  in a streaming manner.
